Software-defined massive multi-input multi-output (mimo)

ABSTRACT

Disclosed are various embodiments for providing a spectrally efficient communication network using clustered devices and virtualized resources in a multi-input multi-output (MIMO) environment. A plurality of remote radio heads (RRHs) can be connected to a central base band unit (BBU) pool of a software-defined network (SDN) associated with the communication network. A procedure can be performed to yield a design for software-defined massive MIMO subject to a plurality of constraints. The design provides a plurality of clusters comprising the RRHs and an association of user devices to the clusters. Examples of initiating implementation of the design by the SDN are provided.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of, U.S. ProvisionalApplication No. 62/849,528, filed on May 17, 2019, entitled“SOFTWARE-DEFINED MASSIVE MULTI-INPUT MULTI-OUTPUT (MIMO),” the entirecontents of which is hereby incorporated herein by reference.

BACKGROUND

The search for higher data capacity in communication networks has led toimprovements such as massive multi-input multi-output (MIMO) whichallows system capacity to be theoretically increased by simplyinstalling additional antennas to remote radio heads (RRHs). However,availability of massive channel state information (CSI) at thetransmitter side as well as co-channel interference from aggressivereuse greatly limit the spectral efficiency of massive MIMO.Software-defined networking approaches can minimize some but not all ofthese drawbacks, for example by enabling coordination amongdensely-deployed RRHs equipped with a large number of antennas.Communication networks that implement conventional massive MIMO orsoftware-defined networking approaches suffer from reduced spectralefficiency due to availability of massive CSI, co-channel interference,intra-/inter-cluster and pilot contamination induced interference.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the embodiments and the advantagesthereof, reference is now made to the following description, inconjunction with the accompanying figures briefly described as follows:

FIG. 1 illustrates a software-defined massive MIMO framework includingan architecture with optimization or improvement of clustering ofdistributed densely-deployed RRHs according to various embodiments ofthe present disclosure.

FIG. 2A illustrates a structure for dividing time-frequency wirelessresources into frames according to various embodiments of the presentdisclosure.

FIG. 2B illustrates a procedure for dynamic RRH clustering according tovarious embodiments of the present disclosure.

FIG. 3 shows a graph illustrating ergodic achievable rates for differentuser numbers according to various embodiments of the present disclosure.

FIG. 4 shows a graph illustrating user sum-rates for different antennanumbers N/K according to various embodiments of the present disclosure.

FIG. 5 illustrates an example flowchart of certain functionalityimplemented by portions of the software-defined massive MIMO frameworkof FIG. 1 according to various embodiments of the present disclosure.

FIG. 6 is a schematic block diagram that illustrates an examplecomputing environment employed in the software-defined massive MIMOframework of FIG. 1 according to various embodiments of the presentdisclosure.

The drawings illustrate only example embodiments and are therefore notto be considered limiting of the scope described herein, as otherequally effective embodiments are within the scope and spirit of thisdisclosure. The elements and features shown in the drawings are notnecessarily drawn to scale, emphasis instead being placed upon clearlyillustrating the principles of the embodiments. Additionally, certaindimensions may be exaggerated to help visually convey certainprinciples. In the drawings, similar reference numerals between figuresdesignate like or corresponding, but not necessarily the same, elements.

DETAILED DESCRIPTION

Disclosed herein are various examples related to providing a spectrallyefficient communication network using clustered devices and virtualizedresources in a massive multi-input multi-output (MIMO) environment.Massive MIMO can include a base station or transmitter side resource,for example, that utilizes more than eight antennas (and sometimes asmany as 128, 256, or more), and can also include user equipment devices(UEs) that utilize around eight antennas. Availability of massivechannel state information (CSI) at the transmitter side as well asco-channel interference from aggressive reuse greatly limit the spectralefficiency of massive MIMO such as when used as an enabling technologyin a 5G and beyond (5G&B) communication network. Software-definednetworking can minimize some of these drawbacks (e.g., by virtualizingresources, providing centralized control, or facilitating theimplementation and aggregation of virtual base stations (VBSs) at thecentral base band unit (BBU) pool). Examples of a wireless architectureand features for applying software-defined networking to wirelessdomains are described by I. F. Akyildiz, P. Wang, and S.-C. Lin in“SoftAir: A software defined networking architecture for 5G wirelesssystems,” Computer Networks, vol. 85, pp. 1-18, 2015, which isincorporated by reference herein in its entirety. The SoftAir approachcan provide an architecture that enables coordination amongdensely-deployed remote radio heads (RRHs) equipped with a large numberof antennas, such as by clustering RRHs and/or providing low-latencyhigh-bandwidth links to connect RRHs to the BBU pool and supportaccurate, high resolution synchronization among RRHs. The examplesdisclosed herein can enhance macro-diversity (e.g., network) massiveMIMO in a software-defined cellular architecture.

A software-defined massive MIMO is disclosed herein that providesdynamic macro-diversity in massive MIMO with respect to a time-varyingdistribution of users of a communication network. The software-definedmassive MIMO includes a procedure that identifies a configuration ofresources and an association of the users to the configuration toprovide spectral efficiency to the communication network. In someexamples, a computing device defines a configuration of clusters formedfrom RRHs available to the communication network, and an association ofusers to the clusters. The disclosed procedure can optimize RRHclustering pattern and RRH-user associations while satisfyingsystem-level constraints. An iterative, global search algorithm isdisclosed that exploits genetic algorithms and yields solutions in onlya few rounds. The software-defined massive MIMO can exhibit the positivefeatures of maximizing network capacity by mitigating the impact ofintra-cluster interference, inter-cluster interference, or pilotcontamination induced interference.

In some examples, a system for providing a spectrally efficientcommunication network using clustered devices and virtualized resourcesin a MIMO environment is provided. At least one application, such as adefinition application or a configuration application, is executable inat least one computing device. The at least one application can causethe computing device to define a configuration of clusters formed fromRRHs available to a communication network, and an association of usersto the clusters to jointly mitigate impact of interference and pilotcontamination. The at least one application can also cause theconfiguration of the RRHs into the clusters, and cause the associationof users to the clusters. The system achieves a sum-rate improvement inevery time slot by dynamically forming the clusters.

In other examples, a method is provided. The method includes identifyingresources that are available to a communication network. Thecommunication network can be associated with a software-defined network,and as such can include RRHs, virtual base stations (VBSs), and/or baseband units (BBUs). The method also includes identifying users associatedwith the communication network. The method further includes determininga configuration of the resources and an association of the users to theconfiguration to provide spectral efficiency to the communicationnetwork. The method provides dynamic macro-diversity massive MIMO withrespect to a time-varying distribution of the users. For example, thedetermining can be based at least in part on a genetic algorithm.

In the disclosed concept, it is understood that a number of technicalproblems exist with regard to use of massive MIMO and software-definednetworks as enabling technologies to provide a spectrally efficient 5G&Bcommunication network. Conventional communication networks suffer fromreduced spectral efficiency due to availability of massive channel stateinformation (CSI), co-channel interference, intra-/inter-cluster andpilot contamination induced interference, among other technical problemsevident from the discussion herein. The methods and systems disclosedsolve one or more technical problems by implementing a procedure thatcan search for a configuration of resources and an association of usersto the configuration to provide spectral efficiency to the communicationnetwork. The disclosure further solves a technical problem by causingthe configuration of the resources and the association of the users tothe resources following applying the procedure to determine a design fora software-defined massive MIMO to provide an improved spectralefficiency to the communication network.

INTRODUCTION

As a key enabling technology for 5G&B systems, massive MIMO allows thesystem capacity to be theoretically increased by simply installingadditional antennas to RRHs. However, this innovative technology cannotsupport higher data capacity without accurate channel state informationand interference handling, especially for multi-cell scenarios. In thisdisclosure, the dynamic macro-diversity (e.g., network) massive MIMO istreated from the perspective of software-defined cellular architecture.The so-called software-defined massive MIMO is introduced, whichdynamically coordinates highly-deployed RRHs equipped with massiveantennas so that the improved or maximum spectral efficiency can beachieved. First, the software-defined cellular architecture ispresented, where distributed massive antenna systems with centralizedcontrol and time-division duplexing massive MIMO are investigated. Next,in this considered architecture, a rigid analysis of achievable ergodicuser sum-rates is given for macro-diversity massive MIMO schemes. Anoptimization framework of software-defined massive MIMO is furtherdisclosed that optimizes RRH clustering pattern and RRH-userassociations while satisfying system-level constraints. To address theNP-complete problem of the optimal framework design, an iterative,global search algorithm is developed that exploits genetic algorithmsand yields satisfactory solutions in only few rounds. Performanceevaluation validates the efficacy of the disclosed solution whichfacilitates universal frequency reuse for 5G&B wireless networks.

To uphold explosive proliferation of wireless devices and drasticallyincreased mobile traffic, 5G and beyond (5G&B) systems are expected tosupport a 100-fold improvement in user-experienced throughput, targeting10 Gbps peak rates and 100 Mbps cell-edge rates. Facing this evolvedtrend together with scarce radio spectrum, new enabling technologiessuch as massive MIMO have great potential to be exploited. Specifically,using the same radio resources but different spatial patterns of thelarge-scale antenna array, massive MIMO can simultaneously transmithigh-speed data streams to multiple users. However, the availability ofmassive CSI at the transmitter side as well as co-channel interferencefrom aggressive reuse greatly limit the actual spectral efficiency.

Recently, software-defined networking has emerged that decouples thecontrol message plane from the user data plane and efficiently createscentralized network abstraction with the programmability provisioningover the entire network. By applying the software-defined networkinginto wireless domains, a new cellular architecture, namely SoftAir, fornext-generation cellular networks is introduced to enable flexiblearchitectural and algorithm designs. It brings the centralized,decoupling wireless architecture that allows real-time networkinformation accessibility and global optimized control. Thecooperativeness of SoftAir also facilitates the implementation andaggregation of virtual base stations (VBSs) at the central base bandunit (BBU) pool to enhance the system performance via jointorchestration/optimization.

Based on the SoftAir architecture, this disclosure aims to facilitateuniversal frequency reuse in the entire 5G&B system by introducingdynamic massive antenna clustering, which can eliminate inter-clusterinterference and can achieve enhanced or optimal system spectralefficiency. First, while equipping each RRH with a large number ofantennas, the disclosed systems and methods can apply the SoftAirarchitecture to enable an efficient coordination among densely-deployedRRHs and construct distributed massive antenna systems. Due to the meritof channel reciprocity, the time-division duplexing (TDD) massive MIMOscheme can be preferable to the counterpart of the frequency-divisionduplexing (FDD) mode. Next, the disclosed systems and methods provide arigid performance analysis of given RRH clustering systems, formed bygrouping the RRHs into clusters with macro-diversity (e.g., network)massive MIMO. The imperfect channel estimation, pilot contamination,path loss, and antenna correlation are considered, and asymptoticachievable user sum-rate is derived with linear eigenbeamformingprecoders.

The disclosed systems and methods further introduce a software-definedmassive MIMO framework that enhances or maximizes the achievablespectral efficiency while considering constraints for realistic SoftAirand high density RRH deployments. The framework aims at finding adesirable (or the best) RRH clustering pattern and RRH-userassociations, which mitigate the impact of intra-/inter-cluster andpilot contamination induced interference concurrently. Moreover, toaddress the NP-complete problem of optimal framework design, thisdisclosure proposes a procedure including an iterative algorithm (e.g.,genetic algorithm (GA)-based dynamic RRH clustering) operated at the BBUpool, which obtains satisfactory solutions in a fast-convergent manner.Numerical results validate the efficacy of macro-diversity massive MIMOwith densely-deployed RRHs, and confirm the superiority of the discloseddynamic clustering that provides the optimal user sum-rate with givenSoftAir configurations. This work appears to be the first to propose acoherent software-defined massive MIMO framework that can eliminateinter-cluster interference and achieve remarkable sum-rate performancefor 5G&B spectral-efficient networks.

Notations: Throughout this disclosure, bold uppercase and lowercaseletters denote matrices and vectors, respectively (I_(N) denotes theidentity matrix with size N). C denotes the set of complex numbers.

[⋅] denotes the expectation operator. A^(T), A^(H), and trA representthe transpose, Hermitian, and trace of matrix A, respectively.

(m, R) denotes the circular symmetric complex Gaussian distribution withmean m and covariance matrix R.

5G&B Spectral-Efficient Networks A. Distributed Massive Antenna Systems

With reference to FIG. 1, shown is a software-defined massive MIMOframework 100 including an architecture with optimization or improvementof clustering of distributed densely-deployed RRHs according to variousembodiments of the present disclosure. Portions of the software-definedmassive MIMO framework 100 can be implemented using a software-definedcellular architecture, SoftAir, or any suitable software-definednetwork. SoftAir, a software-defined cellular architecture, has beenrecognized as an integrated solution of cloud-RAN (C-RAN) andcoordinated multi-point (CoMP), which decouples data plane and controlplane for centralized network control and has the capability ofmaximizing spectral efficiency based on its open platform. As shown inFIG. 1, SoftAir can include three main parts: (i) the BBU pool, whichhosts and manages VBSs, e.g., virtual machines runningsoftware-implemented baseband processing functions as the PHY/MACprotocols, (ii) RRHs equipped with possibly massive antennas, which arecontrolled by VBSs and serve users' transmissions, and (iii) low-latencyhigh-bandwidth optical fibers, which connect the RRHs to the BBU pooland support accurate, high-resolution synchronization among RRHs.SoftAir can form VBSs associated with any cluster of RRHs to mitigatethe cluster-edge effect (e.g., the users at the edges of a clustersuffer from severe out-of-cluster interference), which can providedelay-free CSI exchange. In other words, SoftAir architecture allows5G&B networks to approach the theoretically-optimal linear scaling ofnetwork capacity by enabling innovative designs ofprecoders/detectors/estimators in the BBU pool due to VBSprogrammability, aggressively deploying a large number of low-cost RRHsfor constructing distributed antenna systems, and facilitating diversecooperation modes among the RRHs.

Let

and

denote the sets of RRHs and users in a cellular network, respectively.Also, let c_(i)⊂

be the ith subset of

, which connects to the BBU pool via a fronthaul link with thepredetermined capacity F_(i). In the cluster c_(i), there are K_(i) RRHsequipped with total N_(i) antennas (e.g., each of the RRHs has a largenumber of N_(i)/K_(i) antennas) to serve a user subset

⊂

. An RRH clustering pattern C is then defined as a collection ofnon-empty disjoint subsets of given

, e.g.,

$\begin{matrix}{C = {\{ {{c_{i};{{\bigcap_{c_{i} \in C}c_{i}} = \varnothing}},{{\bigcup_{c_{i} \in C}c_{i}} \subseteq }} \}.}} & (1)\end{matrix}$

Additional constraints due to the practicability of RRH clustering canbe further applied, e.g., the pair-distances of all the RRHs in eachcluster can be less than a predetermined value from service providers'requests. All possible clustering patterns constitute the pattern set C.

B. TDD Massive MIMO

Making massive MIMO operate in TDD is a promising technique thatacquires timely CSI over FDD. In the TDD mode, due to channelreciprocity, estimation can be done in one direction and used in bothuplink and downlink directions, while FDD utilizes respective estimationand feedback for both directions. Also, the cost of uplink training inTDD increases linearly with the number of active users rather than thatof antennas, perfectly fitting the massive MIMO scenarios. The disclosedsystems and methods focus on the use of TDD massive MIMO schemes inSoftAir, where VBSs in the central BBU pool can easily share CSIassociated with different users in the system. Specifically, thetime-frequency wireless resources can be divided into frames, where aframe consists of T seconds and W Hz and leaves room of S=TWtransmission symbols, as shown in FIG. 2A. In each frame, B≥1 out of theS symbols can be dedicated for uplink pilot signaling; the remaining S−Bsymbols can be used for payload data where 1−κ and κ denote the fixedfractions allocated for uplink and downlink, respectively.

Assume that T and W is within the coherence time and bandwidth of allusers, respectively; thus, all the channels are static in the frames.Let h_(lkiu)∈

^((N) ^(l) ^(/K) ^(l) ^()×1) denote the channel response from user u incluster c_(i) to RRH k in cluster c_(l) in a given frame. By arrangingthe responses to all the RRHs in cluster c_(l), one can model thechannel vector h_(liu) as

$\begin{matrix}{{h_{liu} = {\lbrack {h_{l\; 1{iu}}^{T},\ldots \;,h_{{lK}_{i}{iu}}^{T}} \rbrack^{T} = {{R_{liu}^{1\text{/}2}\zeta_{liu}} \in {\mathbb{C}}^{N_{l} \times 1}}}},} & (2)\end{matrix}$

where

R_(liu)  :=  [h_(liuh_(liu)^(H))] ∈ ℂ^(N_(l) × N_(l))

is deterministic and ζ_(liu)˜

(0, I_(N) _(l) ) is an independent fast-fading channel vector.Preferably, by treating the densely-deployed RRHs in a cluster as adistributed antenna array, and forming a single giant VBS thatincorporates all RRH clusters for full cooperation, the inter-clusterinterference in SoftAir can be mitigated, enabling optimal and universalfrequency reuse factor of one. However, realizing such a fullycooperative system needs to face the realistic network conditions. Thefollowing aims at disclosing a procedure for dynamically forming theVBSs (e.g., by dynamically clustering the densely-deployed RRHs), andanalyzing how much cooperation gain can be achieved by SoftAir.

Macro-Diversity Massive MIMO

This section presents macro-diversity (e.g., network) massive MIMO viadensely-deployed RRHs in SoftAir. This section also investigates channelestimation, downlink data transmissions, and the achievable spectralefficiency.

A. MMSE Channel Estimation

During an uplink training phase in TDD networks, the users in RRHcluster c_(i) transmit mutually orthogonal pilot sequences which allowthe BBU pool to compute the estimate Ĥ_(ii) of the local channel H_(ii).While the same set of orthogonal pilot sequences might be reused amongRRH clusters, the channel estimate can be corrupted by pilotcontamination from adjacent clusters. After correlating the receivedtraining signals Y_(i) ^(tr) with the pilot sequences Ψ_(i), the BBUpool can acquire the noisy observation as

{tilde over (Y)} _(i) ^(tr)=Y_(i) ^(tr)Ψ_(i) ^(H)∈

^(N) ^(i) ^(×|U) ^(i) ^(|):=[{tilde over (y)} _(i1) ^(tr) , . . . , y_(i<U) _(i) _(|) ^(tr)],   (3)

and accordingly can estimate the channel vector h_(iiu). Particularly,the disclosed systems and methods can adopt a minimum mean-square error(MMSE) estimator which gives the MMSE estimate ĥ_(iiu) of h_(iiu) as

$\begin{matrix}\begin{matrix}{{\hat{h}}_{iiu} = {R_{iiu}Q_{iu}{\overset{\sim}{y}}_{iu}^{tr}}} \\{{= {{R_{iiu}{Q_{iu}( {h_{iiu} + {\sum\limits_{l \in L_{iu}}h_{ilu}} + {\frac{1}{\sqrt{\rho_{tr}}}{\overset{\sim}{n}}_{iu}^{tr}}} )}} \sim {{}( {0,\Phi_{iiu}} )}}},}\end{matrix} & (4)\end{matrix}$

where ρ_(tr)>0 denotes the effective training signal-to-noise ratio(SNR) and ñ_(iu) ^(tr) ˜

(0,I_(n) _(i) ), and L_(iu) denotes the set of other clusters that usethe same pilot as the one adopted in cluster c_(i) for user u. ρ_(tr),which can be assumed to be a given parameter, generally depends on thesequence length and transmit power of the pilot. One can also defineΦ_(ilu) and Q_(iu) in Eq. (4) as follows:

$\begin{matrix}{{\Phi_{ilu} = {R_{iiu}Q_{iu}R_{ilu}}};{Q_{iu} = ( {{\frac{1}{\rho_{tr}}I_{N}} + {\sum\limits_{l \in {{\{ i\}}\bigcup L_{iu}}}R_{ilu}}} )^{- 1}}} & (5)\end{matrix}$

Applying the orthogonality of the MMSE estimate, the channel vector canbe further decomposed as h_(iiu)=ĥ_(iiu)+{tilde over (h)}_(iiu), where{tilde over (h)}_(iiu)˜

(0, R_(iiu)−Φ_(iiu)) is the uncorrelated (and also statisticallyindependent) estimation error.

B. Downlink Data Transmission

The received downlink signal y_(iu)∈

of user u in RRH cluster c_(i) can be provided as

$\begin{matrix}\begin{matrix}{y_{iu} = {{\sqrt{\rho}{\sum\limits_{l = 1}^{C}\; {h_{liu}^{H}s_{l}}}} + n_{iu}}} \\{= {{\sqrt{\rho}{\sum\limits_{l = 1}^{C}\; {h_{liu}^{H}( {\sqrt{\lambda_{l}}{\sum\limits_{u^{\prime} = 1}^{_{l}}\; {w_{{lu}^{\prime}}x_{{lu}^{\prime}}}}} )}}} + n_{iu}}} \\{{= {\underset{\underset{{Desired}\mspace{14mu} {signal}}{}}{\sqrt{{\rho\lambda}_{i}}h_{iiu}^{H}w_{iu}x_{iu}} + \underset{\underset{Interference}{}}{\sum\limits_{{({l,u^{\prime}})} \neq {({i,u})}}{\sqrt{{\rho\lambda}_{l}}h_{liu}^{H}w_{{lu}^{\prime}}x_{{lu}^{\prime}}}} + \underset{\underset{Noise}{}}{n_{iu}}}},}\end{matrix} & (6)\end{matrix}$

where ρ>0 denotes the downlink SNR, s_(l)∈

^(N) ^(l) is the transmit vector of cluster C_(l), n_(iu)˜

(0,1) is the receiver noise, w_(iu)∈

^(N) ^(i) is a precoding vector, x_(iu)˜

(0,1) contains the user data symbol, and parameter

$\lambda_{l}\mspace{14mu} \text{:=}\mspace{14mu} \frac{1}{E\lbrack {\frac{1}{_{}}{{tr}( {\sum\limits_{u = 1}^{_{}}\; {{bw}_{lu}w_{lu}^{H}}} )}} \rbrack}$

normalizes the average transmit power per user in cluster c_(l) to

${E\lbrack \frac{\rho \; s_{l}^{H}s_{l}}{_{}} \rbrack} = {\rho.}$

Since users do not have any channel estimate, the disclosed systems andmethods aim at yielding an ergodic achievable data rate. One canconsider a linear precoder of practical interest, namelyeigenbeamforming, which can be defined as w_(iu)=ĥ_(iiu) for u∈

_(i). Hence, by assuming that the average effective channels √{squareroot over (λ_(i))}

[h_(iiu) ^(H)w_(iu)] can be perfectly learned by the user, the ergodicachievable spectral efficiency at user u of RRH cluster c_(i) can begiven as

$\begin{matrix}{R_{iu} = {{\kappa ( {1 - \frac{B}{S}} )}\mspace{14mu} {{\log_{2}( {1 + \eta_{iu}} )}\mspace{14mu}\lbrack {{bit}\text{/}s\text{/}{Hz}} \rbrack}}} & (7)\end{matrix}$

with associated signal-to-interference-plus-noise ratio (SINR)

$\eta_{iu} = {\frac{{\rho\lambda}_{i}{{\lbrack {h_{iiu}^{H}{\hat{h}}_{iiu}} \rbrack}}^{2}}{1 + {{\rho\lambda}_{i}{{var}\lbrack {h_{iiu}^{H}{\hat{h}}_{iiu}} \rbrack}} + {\Sigma_{{({l,u^{\prime}})} \neq {({i,u})}}{\rho\lambda}_{l}{\lbrack {{h_{liu}^{H}{\hat{h}}_{llu}}}^{2} \rbrack}}}.}$

Note that Eq. (7) is obtained as a net ergodic achievable rate under anassumption of block-fading channel models, where the rate loss due tochannel training and the rate for uplink transmissions are bothaccounted.

C. Asymptotic Analysis of Macro-Diversity Massive MIMO

Since the ergodic achievable rate R_(iu) in Eq. (7) is hard to computewith finite system dimensions, the disclosed systems and methods studythe large system limit and accordingly investigate the macro-diversitymassive MIMO effect. The notation N→∞ used in the following refers toN_(i), |

_(i)|→such that lim sup_(N) _(i) |

_(i)|/N_(i)<∞ for all c_(i)∈C. That is, the total antenna size and thenumber of served users in each RRH cluster grow infinitely large whilekeeping a finite ratio between the two values. One can aim at derivingthe deterministic approximation η _(iu) of the SINR η_(iu) with thelinear eigenbeamforming precoder such that

$\begin{matrix}{{R_{iu} - {{\overset{\_}{R}}_{iu}\mspace{14mu} \text{:=}\mspace{14mu} {\kappa ( {1 - \frac{B}{S}} )}\mspace{14mu} {\log_{2}( {1 + {\overset{\_}{\eta}}_{iu}} )}}}\underset{Narrow\infty}{arrow}0.} & (8)\end{matrix}$

Particularly, by respectively examining the signal and interferencepower of η_(iu) with the condition of N→∞ and the properties of largedimensional random matrices,

${\overset{\_}{\eta}}_{iu} = \frac{\frac{{\overset{\_}{\lambda}}_{i}}{N_{i}}{{{tr}\; \Phi_{iiu}}}^{2}}{\frac{1}{\rho} + {\Sigma_{l \neq i}\frac{{\overset{\_}{\lambda}}_{l}}{N_{l}}{{{tr}\; \Phi_{liu}}}^{2}} + {\Sigma_{{({l,u^{\prime}})} \neq {({i,u})}}\frac{{\overset{\_}{\lambda}}_{l}}{N_{l}}{trR}_{liu}\Phi_{{llu}^{\prime}}}}$

where

${\overset{\_}{\lambda}}_{l}\mspace{14mu} \text{:=}\mspace{14mu} {( {\frac{1}{N_{i}{_{i}}}{\sum\limits_{u = 1}^{_{i}}\; {{tr}\; \Phi_{iiu}}}} )^{- 1}.}$

The user sum-rate can also be obtained as Σ_(ci∈c)

R _(iu.)

Case study. A case study is considered with N_(i):=N, ∀c_(i)∈

and the same pilot sequences used among all clusters, and with asimplified channel model

$\begin{matrix}{{\lbrack {h_{{ii}\; 1},\ldots \;,h_{{ii}{_{i}}}} \rbrack = {{\sqrt{\frac{N}{D}}{{A\lbrack {v_{{ii}\; 1},\ldots \;,v_{{ii}{_{i}}}} \rbrack}\lbrack {h_{{li}\; 1},\ldots \;,h_{{li}{_{i}}}} \rbrack}} = {\sqrt{\alpha \frac{N}{D}}{A\lbrack {v_{{li}\; 1},\ldots \;,v_{{li}{_{i}}}} \rbrack}}}},{l \neq i}} & (9)\end{matrix}$

where D:=cN, c∈(0,1] indicates the degree of freedom (DoF) offered bythe channel, A∈

^(N×D) is composed of D≤N columns of an arbitrary unitary N×N matrix,v_(liu)∈

is a standard complex Gaussian vector, and α∈(0,19 accounts for aninter-cluster interference factor. Assume that perfect CSI isguaranteed; there is no channel estimation errors (e.g., the scenarioswith large training SNR as ρ_(tr)»1). η _(iu) is given in a closed formas:

$\begin{matrix}{{\overset{\_}{\eta}}_{iu} = \frac{1}{\underset{\underset{{Pilot}\mspace{14mu} {contamination}}{}}{\alpha ( {\overset{\_}{C} - 1} )} + \underset{\underset{Noise}{}}{\overset{\_}{C}\text{/}\rho \; N} + \underset{\underset{Interference}{}}{{_{i}}{\overset{\_}{C}}^{2}\text{/}D}}} & (10)\end{matrix}$

where C:=1 +α(|CI|−1). The results are obtained via somestraight-forward but tedious calculations with the channel model in Eq.(9). From Eq. (10), the interference mainly depends on the ratio D/|

_(i)| (e.g., the number of DoF per user) rather than directly on thetotal antenna size N. It implies that only when the environment supportssufficient scattering, the interference can be reduced by addingadditional antennas (or RRHs). Moreover, if N, D→∞ at the same speed,the noise and interference will vanish and the pilot contaminationremains as the only performance limitation:

$\begin{matrix}{{{\overset{\_}{\eta}}_{iu}\underset{N,{Darrow\infty},{{{_{i}}\text{/}N}arrow 0}}{arrow}n_{\infty}} = {\frac{1}{\alpha^{2}( {{C} - 1} )}.}} & (11)\end{matrix}$

Then, the achievable spectral efficiency becomes

${}{\kappa ( {1 - \frac{B}{S}} )}\mspace{14mu} {{\log_{2}( {1 + \eta_{\infty}} )}.}$

Note that without pilot contamination (e.g., α=0 or |C|=1), the SINRwill grow to infinity as N, D→∞ Also, if D is a large fixed value, theSINR will approach a smaller value than η_(∞), where adding RRHs doesnot necessarily reduce the interference and can improve the SNR.

Software-Defined Massive MIMO

This disclose introduces dynamic macro-diversity massive MIMO withrespect to time-varying user distribution. Specifically, the disclosedsystems and methods propose a software-defined massive MIMO optimizationframework 100 with the objective to improve or maximize the spectralefficiency, while considering a plurality of constraints (e.g.,system-level constraints due to limited fronthaul capacities, andpossibly high density RRH deployments).

A. Software-Defined Massive MIMO Optimization Framework

Given a possible RRH clustering pattern {c_(i)∈C; C∈C} and the user set{

_(i); U_(ci)U_(i)=

}, one can introduce binary variables I_(uci) for all u∈

, c_(i)∈C where

$\begin{matrix}{I_{{uc}_{i}} = \{ \begin{matrix}{1,{{u \in _{i}};}} \\{0,{u \notin {_{i}.}}}\end{matrix} } & (12)\end{matrix}$

These indicators show the assignment between RRH clusters and users. Toprovide that each user is served by a dedicated RRH cluster, thedisclosed systems and methods can include the following associationconstraint: for each u∈

Σ_(ci∈C)I_(uci)=1. Moreover, as all RRHs are connected to the BBU poolvia fronthaul links, F_(i) is the predetermined link capacity betweenRRH cluster c_(i)∈C and the pool. By neglecting the fronthaul capacityconsumption for transferring beamforming vector (as compared to majorconsumption for data streams) and considering the macro-diversitymassive MIMO effective from high density RRH deployments, thesystem-level constraint due to fronthaul capacity can be formulated as:for each c_(i)∈C,

R _(iu)I_(uci)≤F_(i), where R _(iu) is obtained via Eq. (8). So far,this disclosure has successfully characterized the system-levelconstraints for dynamic macro-diversity massive MIMO. To further realizea spectral-efficient clustering design, this disclosure aims to enhanceor maximize the total achievable data rates at users. The user sum-rateis then provided as

$\begin{matrix}\begin{matrix}{{\overset{\_}{R}}^{tot}:={\sum\limits_{c_{i} \in C}{\sum\limits_{u \in }{{\overset{\_}{R}}_{iu}I_{{uc}_{i}}}}}} \\{= {\sum\limits_{c_{i} \in C}{\sum\limits_{u \in }{{\kappa ( {1 - \frac{B}{S}} )}\mspace{14mu} {\log_{2}( {1 + {\overset{\_}{\eta}}_{iu}} )}{I_{{uc}_{i}}.}}}}}\end{matrix} & (13)\end{matrix}$

Hence, one can define the software-defined massive MIMO framework 100for 5G&B networks as follows.

Definition 1: The Software-Defined Massive MIMO Framework 100. Given5G&B networks with the set C of all possible RRH clustering patterns andthe user set

, the software-defined massive MIMO framework can be defined as

$\begin{matrix}{{{{{{Find}\text{:}\mspace{14mu} C^{*}} \in C};{I_{{uc}_{i}}^{*} \in \{ {0,1} \}}},{\forall{u \in }},{c_{i} \in C}}{{Maximize}\mspace{14mu} {{\overset{\_}{R}}^{tot}( {C;\{ I_{{uc}_{i}} \}} )}}{{{{Subject}\mspace{14mu} {to}\mspace{14mu} \Sigma_{c_{i} \in C}I_{{uc}_{i}}} = 1},{\forall{u \in }}}{{{\Sigma_{u \in }{\overset{\_}{R}}_{iu}I_{{uc}_{i}}} \leq F_{i}},{\forall{c_{i} \in C}}}} & (14)\end{matrix}$

The framework 100 aims at finding the optimal RRH clustering pattern andoptimal assignments between RRH clusters and users, according to thedynamic user distribution, in such a way that the network capacity canbe improved or maximized by jointly mitigating the impact of (i) theintra-cluster interference, (ii) the inter-cluster interference, and(iii) the pilot contamination induced interference. This disclosureproposes a procedure including an iterative algorithm that efficientlyrealizes software-defined massive MIMO and achieves maximum usersum-rate in only few rounds.

B. Dynamic RRH Clustering

The optimal design problem of software-defined massive MIMO isNP-complete, where an optimal solution is very difficult to compute in atimely manner.

Also, due to the complex objective formation (e.g., R ^(tot) ), advancedoptimization techniques based on the derivatives (e.g. the gradientand/or hessian of the objective function) are not applicable. Facingthese challenges, the disclosed systems and methods propose a global,derivative-free search algorithm that can provide satisfactory solutions(even the optimal solution with a high probability) by only fewsearching iterations. The disclosed systems and methods can adopt the GAmethod, a randomized and population-based search technique with theroots in genetic principles. This disclosure provides a GA-based RRHclustering algorithm to solve the NP-complete problem.

For each RRH clustering pattern C∈C, the GA procedures are applied: (i)starting with an initial solution set, denoted by initial populationP_(c)(0); (ii) creating a new solution set P_(c)(1) by performingcertain operations on P_(c)(0); (iii) generating populationsP_(c)(2),P_(c)(3), . . . , until an appropriate stopping criterion isreached. The solution to the clustering improvement or optimization isthen obtained as an element of the last-generation population with thelargest value of the objective function. The details of the disclosedprocedure are provided as follows.

Chromosome coding and initialization. The assignment (e.g., I_(uci)) ofeach user-cluster pair is represented as a gene (alphabet) of a binarychromosome string (e.g., [I_(uci); u∈

,c_(i)∈

]). The length of chromosomes (e.g., the number of elements in thestrings) is set as |

||

|. The initial population P_(c) (0) of chromosomes is with populationsize N. Given the chromosome coding, P_(c)(0) is generated by a randomselection of a feasible chromosome set, in which each chromosomesatisfies the constraints of Σ_(c) _(i) _(∈C)I_(uc) _(i) =1, ∀u∈

and

R_(iu)I_(uc) _(i) ≤F_(i), ∀c_(i)∈C from Eq. (14).

Fitness function and selection. To each chromosome there corresponds afitness value of the objective function, and the GA iterativelyoptimizes these fitness values of populations at each round. Set thefitness values of feasible chromosomes as their respective usersum-rates and zero values for infeasible chromosomes. With C∈C and achromosome [I_(uci); u∈

,c_(i)∈

], the fitness f can be defined as

$\begin{matrix}{{{f( \lbrack I_{{uc}_{i}} \rbrack )} = {\underset{u \in }{\Pi}_{\{{{\Sigma_{c_{i} \in C}I_{{uc}_{i}}} = 1}\}}\underset{c_{i} \in C}{\Pi}_{\{{{\Sigma_{u \in }\mspace{14mu} {\overset{\_}{R}}_{iu}I_{{uc}_{i}}} \leq F_{i}}\}} \times {\sum\limits_{c_{i} \in C}{\sum\limits_{u \in }{{\overset{\_}{R}}_{iu}I_{{uc}_{i}}}}}}},} & (15)\end{matrix}$

where I_(E) denotes the indicator function of event E, and f is anonnegative function. Furthermore, a roulette-wheel selection operationcan be adopted which determines the survival chromosomes for thenext-generation population according to their fitness values.Specifically, the mating pool set M_(c)(t) with the same population sizeN_(p) can be formed from P_(c)(t) using a randomization operation asfollows: each element m^(t) in M_(c)(t) is equal to p^(t) in P_(c)(t)with probability

$\frac{f( p^{t} )}{\Sigma_{p_{i}^{t} \in {P_{C}{(t)}}}{f( p_{i}^{t} )}}.$

In other words, the disclosed systems and methods can select chromosomesinto the mating pool with probabilities proportional to their fitnessvalues.

Evolution: Crossover and mutation. The crossover operation involvesexchanging substrings of two randomly chosen parent chromosomes togenerate a pair of offspring chromosomes. Specifically, one-pointcrossover can be applied with a crossover probability p_(c) at achromosome crossing site, which can be uniformly chosen between 1 andN_(p)−1. Moreover, the mutation operation can be applied which mutates(alters) a gene at a random position in chromosomes with a given smallprobability p_(m). In the case of the binary alphabet, this change cancorrespond to complementing the corresponding bits; simply replace eachbit with probability p_(m) from 0 to 1, or vice versa. As the objectiveis to find the optimal RRH clustering, the mutation probability can beset to very small (e.g., 0.01) such that the mutation operation playsonly a minor role in the GA relative to the crossover operation. Afterapplying these two operations to the mating pool M_(c)(t), the disclosedsystems and methods obtain the new population P_(c)(t+1).

The procedure operations of selection, crossover, mutation, and fitnessevaluation can be iteratively repeated until either (i) the fitnessfunction converges, (ii) a maximum number of generations is reached, or(iii) after a maximum number of stall generations with no fitnessimprovement. The chromosome with maximum fitness can then be taken fromthe last generation as the clustering solution with given C. Finally,the optimal design for software-defined massive MIMO can be yielded byselecting the best C∈C, which provides optimal user sum-rate R ^(tot)*and optimal clustering (C*; {I*_(uci)}). FIG. 2B summarizes thedisclosed GA-based dynamic RRH clustering procedure 250 (e.g., Algorithm1). The steps can include:

   1 for each C ϵ C do  2 | Set t := 0. Generate and evaluate P_(C)(0). 3 | while stopping criterion has not been satisfied do  4 | | SelectM_(C)(t) from P_(C)(t).  5 | | Crossover and mutate M_(C)(t) to form   | | P_(C)(t + 1).  6 | | Set t := t + 1. Evaluate P_(C)(t).  7 | end 8 | Update R^(tot)(C; {I_(uc) _(t) }) from the best of P_(C)(t).  9 end10 Yield (C*; {I_(uc) _(t) *}) = argmax_(CϵC) R ^(tot)(C; {I_(uc) _(t)}).

Performance Evaluation

The performance analysis of macro-diversity massive MIMO can bevalidated and the spectral efficiency achieved by the disclosed dynamicRRH clustering evaluated. Consider a SoftAir system that has 9 deployedRRHs in a three-by-three grid over an area of 2,300×2,300 [m²]. Each RRHis equipped with multiple antennas and is set apart from its closet RRHby a distance of 660 [m]. Monte Carlo simulations have been performedfor each evaluated point.

Regarding uniformly-distributed users around cell edges (e.g., theworst-case scenario), FIG. 3 shows the achievable rates of conventionalmassive MIMO and macro-diversity massive MIMO. In the conventionalscheme, each RRH operates independently with the other RRHs; in themacro-diversity scheme, a static clustering pattern is selected as 4 RRHclusters (e.g., c₁={1,2,4,5}); c₂={3,6}; c₃={7}; c₄={8,9}) withsatisfied fronthaul capacity constraints. Each user is served by the RRHthat is closest to itself via the common user association policy. Also,the theoretical bound is obtained via Eq. (11) with α=0.04 and |C|=4.The result indicates that by grouping RRHs into clusters (even with astatic pattern), the macro-diversity scheme reduces the interferingcells and gives much higher rates with the increasing antenna number perRRH (e.g., more antennas to boost the user received power) than that ofthe conventional scheme. Moreover, given a fixed N/K, when the (total)user number decreases (like |

|_(i)/N 0 in Eq. (11)), each pilot sequence is reused by less users,which in turn decreases the interference and increases the spectralefficiency. The above observations successfully validate the accuracy ofthe disclosed theoretical analysis.

To evaluate the disclosed dynamic clustering, the disclosed systems andmethods investigate the impacts of time-varying user distribution, e.g.,when users move around a geographic area. Regarding possible RRHclustering patterns (e.g., set C), one can consider that thepair-distances of all the RRHs in each cluster should less than apredetermined 940 [m] (e.g., due to frontal capacities). Givenrandomly-distributed mobile users, FIG. 4 shows that the disclosedsoftware-defined massive MIMO via the procedure 250 (e.g., Algorithm 1)can ensure at least 35% sum-rate improvements as compared toconventional massive MIMO. That is, with only 20 generations, thedisclosed procedure 250 can achieve the maximum sum-rate in every timeslot by dynamically forming the optimal RRH clustering. These confirmthe efficacy and adaptiveness of the disclosed dynamic clusteringsolution, which enables the software-defined massive MIMO for 5G&Bsystems.

Referring next to FIG. 5, shown is a flowchart that provides one exampleof the operation of a process 500 according to various embodiments. Itis understood that the flowchart of FIG. 5 provides merely an example ofthe many different types of functional arrangements that may be employedto implement the operation of the portion of the software-definedmassive MIMO framework 100 as described herein. As an alternative, theflowchart of FIG. 5 may be viewed as depicting an example of elements ofa method implemented in the software-defined massive MIMO framework 100(FIG. 1) according to one or more embodiments.

At box 503, the process 500 includes identifying at least one RRH (k) ofa plurality of RRHs

) connected to a central BBU pool (VBSs) of a software-defined network(SDN) associated with a communication network (e.g., 5G&B). In someexamples, c_(i)⊂

is the ith subset of

, which connects to the BBU pool (VBSs) via a fronthaul link with apredetermined capacity (F_(i)). At box 506, the process 500 includesidentifying at least one user device (u) of a plurality of user devices(

) associated with the SDN.

At box 509, the process 500 includes iterating a procedure 250 until atleast one stopping criterion is reached to yield a design (C*; {I*_(uc)_(i) }) for software-defined massive MIMO subject to a plurality ofconstraints comprising at least a system level constraint and anassociation constraint. In some examples, the procedure 250 includesselection, crossover, mutation, and fitness evaluation operations of agenetic algorithm. Examples of the system level constraints include thefronthaul capacity (F_(i)) of the fronthaul links. Examples of theassociation constraint include each one of the plurality of clusters(c_(i)) being dedicated to a subset of the RRHs (c_(i)⊂

) (e.g., for each u∈

, Σ_(c) _(i) _(∈C)I_(uc) _(i) =1).

The at least one stopping criterion of the procedure 250 can include:convergence of a fitness function (f), a predefined number of totalgenerations being reached, or a predefined number of stall generationsbeing reached. The design (C*; {I*_(uc) _(i) }) can maximize a user sumrate (R ^(tot)*) at the user devices (z,96 ).

In some examples, the design (C*; {I*_(uc) _(i) }) provides a pluralityof clusters (c_(i)∈C) comprising a subset of the plurality of RRHs(c_(i)∈

) to mitigate an impact due to intra-cluster interference, inter-clusterinterference, and pilot contamination induced interference to providespectral efficiency

$( {{}{\kappa ( {1 - \frac{B}{S}} )}\mspace{14mu} {\log_{2}( ~\eta_{\infty} )}} )$

to the communication network. The design (C*; {I_(uc) _(i) }) alsoprovides an association (e.g., I_(uc) _(i) , or {I*_(uc) _(i) }) of userdevices (

) to the plurality of clusters (c_(i)).

At box 512, the process 500 includes causing the SDN to implement thedesign (C*; {I*_(uc) _(i) }) or initiating implementation of the design(C*; {I*_(uc) _(i) }) by the SDN. In some examples, initiatingimplementation of the design (C*; {I*_(uc) _(i) }) comprises causing atleast one computing device 600 (FIG. 6) to associate the user devices (

) to the plurality of clusters (C*) according to the association({I*_(uc) _(i) }). Thereafter the process can proceed to completion.

Turning to FIG. 6, an example hardware diagram of a general purposecomputer 600 is illustrated. Any of the processed, techniques, andmethods discussed herein may be implemented, in part, using one or moreelements of the general purpose computer 600. The computer 600 includesa processor 610, a Random Access Memory (“RAM”) / a Read Only Memory(“ROM”) 620, an Input Output (“I/O”) interface 630, a memory device 640,and a network interface 650. The elements of the computer 600 arecommunicatively coupled via a bus 602.

The processor 610 comprises any known general purpose arithmeticprocessor or Application Specific Integrated Circuit (“ASIC”). TheRAM/ROM 620 comprise any known random access or read only memory devicethat stores computer-readable instructions to be executed by theprocessor 610. The memory device 630 stores computer-readableinstructions thereon that, when executed by the processor 610, directthe processor 610 to execute various aspects of the present disclosuredescribed herein. When the processor 610 comprises an ASIC, theprocesses described herein may be executed by the ASIC according to anembedded circuitry design of the ASIC, by firmware of the ASIC, or bothan embedded circuitry design and firmware of the ASIC. As a non-limitingexample group, the memory device 630 comprises one or more of an opticaldisc, a magnetic disc, a semiconductor memory (i.e., a semiconductor,floating gate, or similar flash based memory), a magnetic tape memory, aremovable memory, combinations thereof, or any other known memory meansfor storing computer-readable instructions. The network interface 650comprises hardware interfaces to communicate over data networks. The I/Ointerface 630 comprises device input and output interfaces such askeyboard, pointing device, display, communication, and other interfaces.The bus 602 electrically and communicatively couples the processor 610,the RAM/ROM 620, the I/O interface 630, the memory device 640, and thenetwork interface 650 so that data and instructions may be communicatedamong them.

In operation, the processor 610 is configured to retrieve at least oneapplication comprising computer-readable instructions stored on thememory device 640, the RAM/ROM 620, or another storage means, and copythe computer-readable instructions to the RAM/ROM 620 for execution, forexample. The processor 610 is further configured to execute thecomputer-readable instructions to implement various aspects and featuresof the present disclosure. For example, the processor 610 may be adaptedand configured to execute the processes described above, including theprocesses described as being performed as part of a software-definedmassive MIMO framework 100, a genetic algorithm, or a software-definednetwork (SDN). Also, the memory device 640 may store identification datafor the SDN, or for resources associated with the SDN including the RRHsand configurations of clusters formed from individual subsets of theRRHs. The memory device 640 may also store data about constraints,identifications of user devices, and associations of the user devices tothe clusters.

It should be emphasized that the described embodiments of the presentdisclosure are merely possible examples of implementations set forth fora clear understanding of the principles of the disclosure. Manyvariations and modifications may be made to the above-describedembodiment(s) without departing substantially from the spirit andprinciples of the disclosure. All such modifications and variations areintended to be included herein within the scope of this disclosure andprotected by the following claims.

It should be noted that ratios, concentrations, amounts, and othernumerical data may be expressed herein in a range format. It is to beunderstood that such a range format is used for convenience and brevity,and thus, should be interpreted in a flexible manner to include not onlythe numerical values explicitly recited as the limits of the range, butalso to include all the individual numerical values or sub-rangesencompassed within that range as if each numerical value and sub-rangeis explicitly recited. The term “about” can include traditional roundingaccording to significant figures of numerical values. In addition, thephrase “about ‘x’ to ‘y’” includes “about ‘x’ to about ‘y’”.

1. A system, comprising: at least one computing device coupled to anetwork; at least one application executable in the at least onecomputing device, the at least one application causing the at least onecomputing device to: define a configuration of a plurality of clustersformed from individual subsets of a plurality of remote radio heads(RRHs) available to a communication network and an association of userdevices to the plurality of clusters, where the defined configurationand association mitigates impact of interference and pilotcontamination; configure the individual subsets of the plurality of RRHsinto the plurality of clusters based upon the defined configuration; andassociate the user devices to the plurality of clusters based upon thedefined association.
 2. The system of claim 1, wherein the systemprovides dynamic macro-diversity massive MIMO with respect to atime-varying distribution of the user devices.
 3. The system of claim 1,wherein defining the configuration comprises the at least oneapplication further causing the at least one computing device to iteratea procedure until at least one stopping criterion is reached.
 4. Thesystem of claim 1, wherein the system achieves a sum-rate improvement inevery time slot by dynamically forming the plurality of clusters.
 5. Amethod, comprising: identifying resources available to a communicationnetwork; identifying user devices associated with the communicationnetwork; and determining a configuration of the resources and anassociation of the user devices to the configuration to provide spectralefficiency to the communication network.
 6. The method of claim 5,wherein the determining is based at least in part on a geneticalgorithm.
 7. The method of claim 5, wherein the communication networkis associated with a software-defined network.
 8. The method of claim 5,wherein the resources comprise at least one of: remote radio heads(RRHs), virtual base stations (VBSs), and base band units (BBUs).
 9. Themethod of claim 5, wherein the method provides dynamic macro-diversitymassive MIMO with respect to a time-varying distribution of the userdevices.
 10. The method of claim 5, further comprising: configuring theresources based at least in part on the configuration; and associatingthe user devices based at least in part on the association.
 11. Asystem, comprising: at least one computing device coupled to a network;at least one application executable in the at least one computingdevice, the at least one application causing the at least one computingdevice to: identify a plurality of remote radio heads (RRHs) connectedto a central base band unit (BBU) pool of a software-defined network(SDN) associated with a communication network, the plurality of RRHsconnected to the BBU pool via a plurality of fronthaul links; identify aplurality of user devices associated with the SDN; iterate a procedureuntil at least one stopping criterion is reached to yield a design forsoftware-defined massive MIMO subject to a plurality of constraintscomprising at least a system level constraint and an associationconstraint; and initiate implementation of the design by the SDN. 12.The system of claim 11, wherein the procedure comprises selection,crossover, mutation, and fitness evaluation operations.
 13. The systemof claim 11, wherein the at least one stopping criterion comprises:convergence of a fitness function, a predefined number of totalgenerations being reached, or a predefined number of stall generationsbeing reached.
 14. The system of claim 11, wherein the design maximizesa user sum rate at the user devices.
 15. The system of claim 11, whereinthe system level constraint comprises a fronthaul capacity of thefronthaul links.
 16. The system of claim 11, wherein the design providesa plurality of clusters comprising a subset of the plurality of remoteradio heads (RRHs) to mitigate an impact due to intra-clusterinterference, inter-cluster interference, and pilot contaminationinduced interference to provide spectral efficiency to the communicationnetwork.
 17. The system of claim 16, wherein the design provides anassociation of user devices to the plurality of clusters.
 18. The systemof claim 16, wherein the association constraint comprises each one ofthe plurality of clusters being dedicated to the subset of the pluralityof remote radio heads (RRHs).
 19. The system of claim 18, whereininitiate implementation of the design by the SDN comprises the at leastone application further causing the at least one computing device toassociate the user devices to the plurality of clusters according to theassociation.
 20. The system of claim 16, wherein the plurality ofconstraints further comprises a pair-distance constraint specifying thatpair-distances of RRHs in each of the plurality of clusters should beless than a predetermined value.